uzasadnij

[snowinska91]

Uzasadnij, że
a) \(\sqrt[6]{81}= \sqrt[3]{9}\)
b)\(\sqrt[12]{625}= \sqrt[3]{5}\)
c)\(\sqrt[4]{3} \cdot \left( \sqrt[4]{27} +3\sqrt[4]{3} \right)=3+3 \sqrt{3}\)

[eresh]

Uzasadnij, że
a) \(\sqrt[6]{81}= \sqrt[3]{9}\)
b)\(\sqrt[12]{625}= \sqrt[3]{5}\)
c)\(\sqrt[4]{3} \cdot \left( \sqrt[4]{27} +3\sqrt[4]{3} \right)=3+3 \sqrt{3}\)

\(\sqrt[6]{81}= 81^{\frac{1}{6}}=9^{\frac{2}{6}}=9^{\frac{1}{3}}=\sqrt[3]{9}\\
\sqrt[12]{625}=625^{\frac{1}{12}}=(5^4)^{\frac{1}{12}}=5^{\frac{1}{3}}=\sqrt[3]{5}\\
\sqrt[4]{3} \cdot \left( \sqrt[4]{27} +3\sqrt[4]{3} \right)=\sqrt[4]{3\cdot 27}+3\sqrt[4]{3\cdot 3}=\sqrt[4]{3^4}+3\sqrt[4]{3^2}=3+3\sqrt{3}\)